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Dividers & Compasses

Dividers and compasses are drawing instruments that have been used since antiquity to measure distances, transfer lengths from one drawing to another, and draw circles. The Greek mathematician, Euclid, limited the constructions in his Elements of Geometry to those that could be done with an unmarked straight edge and rudimentary compass. Ancient Roman dividers survive in the collections of the British Museum. Before the 18th century, when one leg was modified to take a pen or pencil point, compasses had two sharp points, like dividers. The user scratched the writing surface in the shape of a circle and then inked the scratches.

If you have used your thumb and forefinger to compare a distance between two points on a map with the mileage scale in the map's legend box, then you have used your body as a pair of dividers. This instrument typically has two legs, hinged at one end and with sharp points at the other end. It can be used by itself or in combination with a calculating instrument, such as a sector.

Most Americans probably last held a drawing compass in elementary school. It also usually has two legs, one with a sharp point for holding the instrument in place and one with a pen or pencil point for tracing out a circle. Some compasses have interchangeable points, so that they can also function as dividers. Both types of objects were widely sold individually or in sets of drawing instruments from the 17th through the 20th centuries. Instrument makers, such as Nicolas Bion in the 18th century and William Ford Stanley in the 19th century, provided detailed descriptions of the different types of dividers and compasses suitable for different drawing tasks. By the 20th century, manufacturers and retailers devoted considerable space in their catalogs to these instruments.

The approximately five dozen objects and related documentation in the NMAH mathematics collections illustrate the diversity of forms of dividers and compasses, as well as the proliferation of the instruments when a mass market opened around 1900. This expansion arose in part from a new ability to manufacture large numbers of high-quality products to sell for low prices. It also reflects the use of dividers and compasses in school and university mathematics. During the 19th century, technical drawings became a routine part of American engineering practice. Drafting was widely taught in engineering schools, and, with the advent of high schools, as part of vocational training for boys and a handful of girls. Budding engineers and mechanics would own a set of drawing instruments that included one or more compasses and a pair of dividers. Compasses also continued to be employed in the geometry classroom. In the 21st century, dividers and compasses are almost exclusively used in primary and secondary education, with computer-aided design preferred over drawing by hand in professional practice.

The objects in the collection were made from brass, German silver, aluminum, steel, and other metals; wood; and plastic. They were made in Germany, Switzerland, Great Britain, the United States, France, and Japan between the early 18th century and the end of the 20th century. They came to the museum from individual donors, other government agencies, manufacturers, and universities. One patent model is in the collection. On the following pages, you may explore dividers, compasses, instruments used as both dividers and compasses, and two specialized forms of dividers and compasses. Although there are not many academic books and articles specifically devoted to dividers and drawing compasses, the page of resources offers suggestions for further learning about the general history of drawing instruments.

Histories of drawing instruments typically include calipers alongside dividers and compasses. Mathematicians and engineers used calipers to measure round objects, such as artillery shot, and places that might hold round objects, such as the inside of a cannon barrel. Since the mathematics collection includes only one pair of calipers, it is shown here.

Acknowledgements

The digitization of this group of artifacts was made possible through the generous support of Edward and Diane Straker.